This is very much a "fine-tuning" area of knives. Bear in mind that any sharp knife, regardless of symmetry will out perform a dull knife at any task.
Okie dokie, here we go.
Assuming equal edge angles, an ayssemetry no greater than 70:30 (Misono UX-10) doesn't make much difference at all. After that, the knife begins to steer (more about steering later) -- mostly for the wrong handed user, but for the correct handed user as well.
A Japanese knife is intended for a single side edge is ground asymmetrically at the knife faces as well at the edge. The edge side is ground at an angle for all of some portion of the blade (saber, partial saber grind), while the back is flat or slightly concave. This makes it impossible for a wrong handed user to guide the knife accurately by holding it against the off hand, and using the off hand as a guide ("claw").
Steering is the tendency for a knife to twist or for the point to go left or right. It's exacerbated by a tight grip. The harder you squeeze the knife, the less control you have. The more you line up the point with hand, wrist, forearm and elbow, the straighter your cut will be.
Assuming a good grip, and otherwise good technique, asymmetry is helpful in creating finer "sticks" (i.e., alumette, baton, batonet, julienne), but this is a very fine point. It's much more about the cook than the knife.
Assuming a good grip, and otherwise good technique, asymmetry makes deep slicing, prime-rib e.g., difficult.
FWIW, the key to thin slicing is not the edge geometry, but learning to feel the outside face of the food, with the knife in the cut. To the extent that equipment plays a role at all, factors other than symmetry are more important -- flex and blade width, for instance.
Asymmetry is helpful in cutting through, rather than tearing, soft fibers -- as in raw fish flesh. In other words, given the same level of sharpness, a highly asymmetric edge will act slightly sharper. That is, with objective "sharpness" defined by the average width of the edge, the lack of deviation from that average, and the trueness of the edge across the langitudinal and latitudinal axes. However, a very sharp slicer beveled to 15* edges with 50/50 symmetry will certainly outperform a moderately sharp yanigaba beveled to a single 10* edge.
Hope this helps,